Gravity gradiometers have existed for many years and are used to measure variations in the gradients of the earth's gravitational field. Gravity gradiometers may be used in exploration for minerals and hydrocarbons, since deposits of these things in the earth, and variations in the underground structure containing the deposits, produce variations in gravity and in the gravitational gradients which if interpreted correctly can lead to valuable discoveries. The ability to operate a gravity gradiometer in a moving vehicle is desirable, since doing so can greatly decrease the amount of time needed to carry out a survey of a given site.
The variations in the gravity gradients which must be measured are extremely small in magnitude and therefore require very sensitive, low noise instruments with very repeatable response characteristics. Moreover, when the gravity gradiometer is mounted in a moving vehicle, the signals due to these gravity gradient changes are very small in comparison to the undesirable responses of the instrument produced by accelerations and rotational motions of the vehicle on which the instrument is mounted.
The reported performance of present commercially operating airborne gravity gradiometers is currently limited to an error level of about three to four Eotvos (1 E=a gradient of 10−9 meters per second squared per meter, approximately 10−10 g per meter) at a signal averaging time of six seconds, when operating in very low-turbulence flying conditions, with performance degrading as turbulence increases. Although this performance has been sufficient to hint at the potential usefulness of airborne gravity gradiometry, improvement to a performance level of 1 E averaged once per second is believed to be required for widespread successful application in mineral exploration.
A known form of gravity gradiometer which has the laboratory demonstrated potential to provide this performance gain is the so-called orthogonal quadrupole responder (also referred to here as an OQR, and also known as the cross-component gravity gradiometer). In the OQR, two orthogonally oriented mass quadrupoles (also referred to here as balance beams), each being a body whose mass is distributed in such a way that it has non-equal mass quadrupole moments along two axes that are orthogonal to each other and to a desired rotation axis, are attached to a housing springs whose mutual alignment defines the desired rotation axis, thus comprising quadrupole responders (also sometimes called angular accelerometers). The balance beams rotate differentially (in opposite directions) in response to changes in certain gravity gradient tensor components, but rotate in common mode (both in the same direction) in response to rotational acceleration motions of the housing. Thus, in principle, when the housing is mounted in a vehicle the OQR separates the weak gravity gradient signals from the much larger noise due to vehicle angular accelerations.
Early versions of a rotating version of an OQR gravity gradiometer design have been disclosed by Weber, Zipoy and Forward in U.S. Pat. No. 3,722,284, and by Robert L. Forward, “Future lunar gravity measurements,” Earth, Moon, and Planets, Volume 22, No. 4 (1980) pp. 419-433, and by Lautzenhiser in U.S. Pat. No. 4,215,578. Ho Jung Paik, in “Superconducting tensor gravity gradiometry for satellite geodesy and inertial navigation,” The Journal of the Astronautical Sciences, Volume XXIX, No. 1, pp. 1-18, January-March 1981, presented a description of a Cross Component Gradiometer (discussion on p. 7, and FIG. 4), which is topologically equivalent to Forward's design, but which utilizes superconducting materials, inductive gap-sensing coils and SQUID transducers in order to achieve a high signal to noise ratio without needing to have the entire instrument rotate. A later version also employing superconducting materials is disclosed by Van Kann and Buckingham in U.S. Pat. No. 5,668,315, and is described as an OQR by Van Kann et al., “Laboratory tests of a mobile superconducting gravity gradiometer”, Physica B, Volume 165 (1990) pp. 93-94. In Moody, Paik & Canavan, “Principle and performance of a superconducting angular accelerometer”, Review of Scientific Instruments, Volume 74, Issue 3 (2003) pp. 1310-1318, details of a built and tested superconducting angular accelerometer are described, a pair of which can be used to form an OQR gravity gradiometer.
Existing examples of OQR gravity gradiometers make use of cryogenic temperatures, both to permit the use of SQUID (Superconductive Quantum Interference Device) based detection of the quadrupole responders' motion, and to achieve almost perfectly elastic behavior in the torsional springs on which the mass quadrupoles are mounted. Van Kann and Buckingham described one such OQR gravity gradiometer in U.S. Pat. No. 5,668,315. Another version is first described in E. R. Canavan, M. V. Moody, H. J. Paik, R. V. Duncan, and J. A. Demko “Superconducting Gravity Gradiometer for Airborne Survey,” presented at the American Geophysical Union Fall Meeting (San Francisco, December, 1995), and further detailed in Moody, M. V. and Paik, H. J., “A superconducting gravity gradiometer for inertial navigation”, in Proc. IEEE 2004 Position Location and Navigation Symposium (PLANS 2004), April 2004, pp. 775-781. Still, another version is described in French, J. B. et al., U.S. Pat. No. 7,360,419. At temperatures significantly above cryogenic temperatures, including standard room temperature, all polycrystalline materials exhibit creep and hysteresis effects which degrade instrument response repeatability (which is, for example, why some high quality gravity meters are constructed of amorphous fused quartz, which exhibits much lower creep and hysteresis).
Current non-rotating OQR-type gravity gradiometers join their balance beams to their housings using springs which are in the form of a “microscopically” thick web. Being very thin, such a web will have a small cross-sectional area, resulting in large stresses in the web material in response to housing accelerations; hence such webs are fragile and are prone to breaking. It has proven difficult to achieve requisite dimensional tolerances when manufacturing that type of web flexure. Importantly, a web, when stressed by accelerations of the moving aircraft or vehicle, will undergo anisoelastic deformation (as described below), leading to undesirable nonlinear errors (sometimes referred to as noise) being imposed on the gradiometer signal.